Control Systems
State Variable Analysis
Practice questions from State Variable Analysis.
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IncorrectConsider a system where , and are three internal state signals and is the input signal. The differential equations governing the system are given by
Which of the following statements is/are TRUE?
The signals , and are bounded for all bounded inputs
There exists a bounded input such that at least one of the signals , , and is unbounded
There exists a bounded input such that the signals , and are unbounded
The signals , and are unbounded for all bounded inputs
Option (A), If bounded input
Say unit step function,
False, statement.
Option (B), As check above for bounded i/p of unit step function, are unbounded.
Hence, True statement.
Option (C), if u(t) is bounded, then all poles of will lies in LHS of -plane.
Thus, all poles of will also lies in LHS of s-plane.
For bounded, always bounded.
False, statement.
option (D), As check above, if always bounded,
then also always bounded.
Hence, option (b) is correct.
Consider a system S represented in state space as
Which of the state space representations given below has/have the same transfer function as that of S?
Opt (a)
(a) and (c) are correct.
The state equation of a second order system is is the initial condition.
Suppose and are two distinct eigenvalues of A and and are the corresponding eigenvectors. For constants and , the solution, , of the state equation is
The correct option is 1
Concept:
Given:
If is the eigenvalue of matrix A then .
As there are 2 eigenvalues and of matrix A , the solution of the state equation will be, Hence, the correct option is (a).
